{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 02. Small Worlds and Large Worlds\n",
    "\n",
    "#### Chapter Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import stats\n",
    "import random\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "np.set_printoptions(suppress=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Code 2.1**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.  , 0.15, 0.4 , 0.45, 0.  ])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ways = np.array([0, 3, 8, 9, 0])\n",
    "ways/sum(ways)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Code 2.2**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.16406250000000006"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.binom.pmf(k=6, n=9, p=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That number is the relative number of ways to get 6 water (in our globe-tossing model) holding `p` at 0.5.\n",
    "\n",
    "Much later in the book, in Chapter 10, we’ll see that the binomial distribution is rather special, because it represents the maximum entropy way to count binary events. “Maximum entropy” means that the distribution contains no additional information other than: There are two events, and the probabilities of each in each trial are `p` and `1 − p`. Chapter 10 explains this in more detail, and the details can certainly wait."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Code 2.3** Grid Approximation\n",
    "\n",
    "1. Define the grid. This means you decide how many points to use in estimating the posterior, and then you make a list of the parameter values on the grid.\n",
    "\n",
    "2. Compute the value of the prior at each parameter value on the grid.\n",
    "\n",
    "3. Compute the likelihood at each parameter value.\n",
    "\n",
    "4. Compute the unstandardized posterior at each parameter value by multiplying the prior by the likelihood.\n",
    "\n",
    "5. Finally, standardize the posterior by dividing the values by the sum of all values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def grid_approximation(n_success, n_trials, n_points):\n",
    "    # Define the grid.\n",
    "    p_grid = np.linspace(0, 1, n_points)\n",
    "    \n",
    "    # Define the prior.\n",
    "    # For a uniform prior.\n",
    "    prior = np.repeat(1, n_points)\n",
    "    \n",
    "    # Compute the likelihood at each parameter value.\n",
    "    likelihood = stats.binom.pmf(n_success, n_trials, p_grid)\n",
    "    \n",
    "    # Compute the unstandardized posterior at each parameter value.\n",
    "    posterior_unstd = likelihood * prior\n",
    "    \n",
    "    # Standardize the posterior.\n",
    "    posterior_std = posterior_unstd / np.sum(posterior_unstd)\n",
    "    \n",
    "    # We want both the grid and posterior for plotting.\n",
    "    return p_grid, posterior_std"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "p_grid, posterior = grid_approximation(n_success=6, n_trials=9, n_points=500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(15, 8))\n",
    "ax.plot(p_grid, posterior, color='grey')\n",
    "ax.fill_between(p_grid, posterior, color='lightseagreen', alpha=.5)\n",
    "ax.set_title('Grid Approximation After 6 Successes in 9 Tosses - 500 Points', fontsize=20)\n",
    "ax.set_xlabel('Proportion of Earth that is Water', fontsize=15)\n",
    "ax.set_ylabel('Posterior Probability', fontsize=15);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try the prior where we assume a 0% chance of the true proportion of water being less than 50%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def grid_approximation(n_success, n_trials, n_points):\n",
    "    p_grid = np.linspace(0, 1, n_points)\n",
    "    #prior = np.repeat(1, n_points)\n",
    "    prior = (np.linspace(0, 1, n_points) >= .5).astype(int)\n",
    "    likelihood = stats.binom.pmf(n_success, n_trials, p_grid)\n",
    "    posterior_unstd = likelihood * prior\n",
    "    posterior_std = posterior_unstd / np.sum(posterior_unstd)\n",
    "    return p_grid, posterior_std"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p_grid, posterior = grid_approximation(n_success=6, n_trials=9, n_points=500)\n",
    "fig, ax = plt.subplots(figsize=(15, 8))\n",
    "ax.plot(p_grid, posterior, color='grey')\n",
    "ax.fill_between(p_grid, posterior, color='lightseagreen', alpha=.5)\n",
    "ax.set_title('Grid Approximation After 6 Successes in 9 Tosses - 500 Points', fontsize=20)\n",
    "ax.set_xlabel('Proportion of Earth that is Water', fontsize=15)\n",
    "ax.set_ylabel('Posterior Probability', fontsize=15);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### End Chapter Problems"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Easy**\n",
    "\n",
    "**2E1.** Which of the expressions below correspond to the statement: *the probability of rain on Monday*?\n",
    "\n",
    "1. `Pr(rain)`\n",
    "2. **`Pr(rain|Monday)`**\n",
    "3. `Pr(Monday|rain)`\n",
    "4. `Pr(rain, Monday)/Pr(Monday)`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2E2.** Which of the following statements corresponds to the expression Pr(Monday|rain)?\n",
    "\n",
    "1. The probability of rain on Monday.\n",
    "2. The probability of rain, given that it is Monday.\n",
    "3. **The probability that it is Monday, given it is raining.**\n",
    "4. The probability that it is Monday and that it is raining. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2E3.** Which of the expressions below correspond to the statement: *the probability that it is Monday, given that it is raining*?\n",
    "\n",
    "1. **`Pr(Monday|rain)`**\n",
    "2. `Pr(rain|Monday)`\n",
    "3. `Pr(rain|Monday)*Pr(Monday)`\n",
    "4. **`Pr(rain|Monday)*Pr(Monday/Pr(rain)`**\n",
    "5. `Pr(Monday|rain)*Pr(rain)/Pr(Monday)`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2E4.** The Bayesian statistician Bruno de Finetti (1906 - 1985) began his book on probability theory with the declaration: \"PROBABILITY DOES NOT EXIST.\" The capitals appeared in the original, so I imagine de Finetti wanted us to shout this statement. What he meant is that probability is a device for describing uncertainty from the perspective of an observer with limited knowledge; it has no objective reality. Discuss the globe tossing experiment from the chapter, in light of this statement. What does it mean to say \"the probability of water is 0.7\"?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Medium**\n",
    "\n",
    "**2M1.** Recall the globe tossing model from the chapter. Compute and plot the grid approximate posterior distribution for each of the following sets of observations. In each case, assume a uniform prior for `p`. \n",
    "\n",
    "1. W,W,W\n",
    "2. W,W,W,L\n",
    "3. L,W,W,L,W,W"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Redefine the grid_approximation function to contain a uniform prior.\n",
    "def grid_approximation(n_success, n_trials, n_points):\n",
    "    p_grid = np.linspace(0, 1, n_points)\n",
    "    prior = np.repeat(1, n_points)\n",
    "    likelihood = stats.binom.pmf(n_success, n_trials, p_grid)\n",
    "    posterior_unstd = likelihood * prior\n",
    "    posterior_std = posterior_unstd / np.sum(posterior_unstd)\n",
    "    return p_grid, posterior_std"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. W,W,W"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p_grid, posterior = grid_approximation(n_success=3, n_trials=3, n_points=500)\n",
    "fig, ax = plt.subplots(figsize=(15, 8))\n",
    "ax.plot(p_grid, posterior, color='grey')\n",
    "ax.fill_between(p_grid, posterior, color='lightseagreen', alpha=.5)\n",
    "ax.set_title('Grid Approximation After 3 Successes in 3 Tosses - 500 Points', fontsize=20)\n",
    "ax.set_xlabel('Proportion of Earth that is Water', fontsize=15)\n",
    "ax.set_ylabel('Posterior Probability', fontsize=15);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. W,W,W,L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p_grid, posterior = grid_approximation(n_success=3, n_trials=4, n_points=500)\n",
    "fig, ax = plt.subplots(figsize=(15, 8))\n",
    "ax.plot(p_grid, posterior, color='grey')\n",
    "ax.fill_between(p_grid, posterior, color='lightseagreen', alpha=.5)\n",
    "ax.set_title('Grid Approximation After 3 Successes in 4 Tosses - 500 Points', fontsize=20)\n",
    "ax.set_xlabel('Proportion of Earth that is Water', fontsize=15)\n",
    "ax.set_ylabel('Posterior Probability', fontsize=15);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3. L,W,W,L,W,W"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p_grid, posterior = grid_approximation(n_success=4, n_trials=6, n_points=500)\n",
    "fig, ax = plt.subplots(figsize=(15, 8))\n",
    "ax.plot(p_grid, posterior, color='grey')\n",
    "ax.fill_between(p_grid, posterior, color='lightseagreen', alpha=.5)\n",
    "ax.set_title('Grid Approximation After 4 Successes in 6 Tosses - 500 Points', fontsize=20)\n",
    "ax.set_xlabel('Proportion of Earth that is Water', fontsize=15)\n",
    "ax.set_ylabel('Posterior Probability', fontsize=15);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2M2.** Now assume a prior for `p` that is equal to zero when p < 0.5 and is a positive constant when p >= 0.5. Again compute and plot the grid approximate posterior distribution for each of the sets of observations in the problem just above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Redefine grid_approximation to contain the prior stated above.\n",
    "def grid_approximation(n_success, n_trials, n_points):\n",
    "    p_grid = np.linspace(0, 1, n_points)\n",
    "    prior = (np.linspace(0, 1, n_points) >= .5).astype(int)\n",
    "    likelihood = stats.binom.pmf(n_success, n_trials, p_grid)\n",
    "    posterior_unstd = likelihood * prior\n",
    "    posterior_std = posterior_unstd / np.sum(posterior_unstd)\n",
    "    return p_grid, posterior_std"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. W,W,W"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p_grid, posterior = grid_approximation(n_success=3, n_trials=3, n_points=500)\n",
    "fig, ax = plt.subplots(figsize=(15, 8))\n",
    "ax.plot(p_grid, posterior, color='grey')\n",
    "ax.fill_between(p_grid, posterior, color='lightseagreen', alpha=.5)\n",
    "ax.set_title('Grid Approximation After 3 Successes in 3 Tosses - 500 Points', fontsize=20)\n",
    "ax.set_xlabel('Proportion of Earth that is Water', fontsize=15)\n",
    "ax.set_ylabel('Posterior Probability', fontsize=15);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. W,W,W,L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p_grid, posterior = grid_approximation(n_success=3, n_trials=4, n_points=500)\n",
    "fig, ax = plt.subplots(figsize=(15, 8))\n",
    "ax.plot(p_grid, posterior, color='grey')\n",
    "ax.fill_between(p_grid, posterior, color='lightseagreen', alpha=.5)\n",
    "ax.set_title('Grid Approximation After 3 Successes in 4 Tosses - 500 Points', fontsize=20)\n",
    "ax.set_xlabel('Proportion of Earth that is Water', fontsize=15)\n",
    "ax.set_ylabel('Posterior Probability', fontsize=15);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3. L,W,W,L,W,W"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p_grid, posterior = grid_approximation(n_success=4, n_trials=6, n_points=500)\n",
    "fig, ax = plt.subplots(figsize=(15, 8))\n",
    "ax.plot(p_grid, posterior, color='grey')\n",
    "ax.fill_between(p_grid, posterior, color='lightseagreen', alpha=.5)\n",
    "ax.set_title('Grid Approximation After 4 Successes in 6 Tosses - 500 Points', fontsize=20)\n",
    "ax.set_xlabel('Proportion of Earth that is Water', fontsize=15)\n",
    "ax.set_ylabel('Posterior Probability', fontsize=15);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2M3.** Suppose there are two globes, one for Earth and one for Mars. The Earth globe is 70% covered in water. The Mars globe is 100% land. Futher suppose that one of these globes, you don't know which, was tossed in the air and produced a \"land\" observation. Assume that each globe was equally likely to be tossed. Show the posterior probability that the globe was the Earth, conditional on seeing \"land\" (`Pr(Earth|Land) = 0.23`)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use Bayes' rule.\n",
    "\n",
    "\\begin{equation*}\n",
    "P(Earth|Land) = \\frac{P(Land|Earth)*P(Earth)}{P(Land)} = \\frac{P(Land|Earth)*P(Earth)}{P(Land|Earth)*P(Earth) + P(Land|Mars)*P(Mars)}\n",
    "\\end{equation*}\n",
    "\n",
    "\\begin{equation*}\n",
    "P(Earth|Land) = \\frac{0.3*0.5}{0.3*0.5 + 1.0*0.5} = 0.23\n",
    "\\end{equation*}\n",
    "\n",
    "And then run a simulation to verify."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "When we've gotten land, the globe was Earth approximately 0.230424% of the time.\n",
      "This is simply 0.3 / (0.3 + 1.0) = 0.230769\n"
     ]
    }
   ],
   "source": [
    "GLOBES = ('Earth', 'Mars')\n",
    "p_land = {'Earth':.3, 'Mars':1}\n",
    "\n",
    "n_sims = 10**6\n",
    "n_land = 0\n",
    "n_earth = 0\n",
    "\n",
    "while n_land < n_sims:\n",
    "    globe = random.choice(GLOBES) \n",
    "    if random.random() <= p_land[globe]:\n",
    "        n_land += 1\n",
    "        \n",
    "        if globe == 'Earth':\n",
    "            n_earth += 1\n",
    "            \n",
    "print(f'When we\\'ve gotten land, the globe was Earth approximately {n_earth/n_land}% of the time.')\n",
    "print(f'This is simply 0.3 / (0.3 + 1.0) = {round(0.3 / (0.3 + 1.0), 6)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2M4.** Suppose you have a deck with only three cards. Each card has two sides, and each side is either black or white. One card has two black sides. The second card has one black and one white side. The third card has two white sides. Now suppose all three cards are placed in a bag and shuffled. Someone reaches into the bag and pulls out a card and places it flat on a table. A black side is shown facing up, but you don’t know the color of the side facing down. Show that the probability that the other side is also black is 2/3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.66639"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CARDS = (('B', 'B'), ('B', 'W'), ('W', 'W'))\n",
    "n_success = 0\n",
    "n_trials = 0\n",
    "\n",
    "while n_trials < 10**6:\n",
    "    card = random.choice(CARDS)\n",
    "    side_num = random.randint(0,1)\n",
    "    color_side_up = card[side_num]\n",
    "    color_side_down = card[1-side_num]\n",
    "\n",
    "    if color_side_up == 'B':\n",
    "        n_trials += 1\n",
    "        if color_side_down == 'B':\n",
    "            n_success += 1\n",
    "        \n",
    "n_success/n_trials"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2M5.** Now suppose there are four cards: B/B, B/W, W/W, and another B/B. Again suppose a card is drawn from the bag and a black side appears face up. Again calculate the probability that the other side is black."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.799802"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CARDS = (('B', 'B'), ('B', 'W'), ('W', 'W'), ('B', 'B'))\n",
    "n_success = 0\n",
    "n_trials = 0\n",
    "\n",
    "while n_trials < 10**6:\n",
    "    card = random.choice(CARDS)\n",
    "    side_num = random.randint(0,1)\n",
    "    color_side_up = card[side_num]\n",
    "    color_side_down = card[1-side_num]\n",
    "\n",
    "    if color_side_up == 'B':\n",
    "        n_trials += 1\n",
    "        if color_side_down == 'B':\n",
    "            n_success += 1\n",
    "        \n",
    "n_success/n_trials"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2M6.** Imagine that black ink is heavy, and so cards with black sides are heavier than cards with white sides. As a result, it’s less likely that a card with black sides is pulled from the bag. So again assume there are three cards: B/B, B/W, and W/W. After experimenting a number of times, you conclude that for every way to pull the B/B card from the bag, there are 2 ways to pull the B/W card and 3 ways to pull the W/W card. Again suppose that a card is pulled and a black side appears face up. Show that the probability the other side is black is now 0.5."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.500029"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CARDS = (('B', 'B'), ('B', 'W'), ('B', 'W'), ('W', 'W'), ('W', 'W'), ('W', 'W'))\n",
    "n_success = 0\n",
    "n_trials = 0\n",
    "\n",
    "while n_trials < 10**6:\n",
    "    card = random.choice(CARDS)\n",
    "    side_num = random.randint(0,1)\n",
    "    color_side_up = card[side_num]\n",
    "    color_side_down = card[1-side_num]\n",
    "\n",
    "    if color_side_up == 'B':\n",
    "        n_trials += 1\n",
    "        if color_side_down == 'B':\n",
    "            n_success += 1\n",
    "        \n",
    "n_success/n_trials"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2M7.** Assume again the original card problem, with a single card showing a black side face up. Before looking at the other side, we draw another card from the bag and lay it face up on the table. The face that is shown on the new card is white. Show that the probability that the first card, the one showing a black side, has black on its other side is now 0.75. Use the counting method, if you can. Hint: Treat this like the sequence of globe tosses, counting all the ways to see each observation, for each possible first card."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.75016"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CARDS = (('B', 'B'), ('B', 'W'), ('W', 'W'))\n",
    "\n",
    "n_success = 0\n",
    "n_trials = 0\n",
    "\n",
    "while n_trials < 10**5:\n",
    "    card_indices_chosen = np.random.choice([0, 1, 2], size=2, replace=False)\n",
    "    first_card = CARDS[card_indices_chosen[0]]\n",
    "    side_num = random.randint(0,1)\n",
    "    first_color_side_up = first_card[side_num]\n",
    "    first_color_side_down = first_card[1-side_num]\n",
    "    \n",
    "    if first_color_side_up == 'B':\n",
    "        \n",
    "        second_card = CARDS[card_indices_chosen[1]]\n",
    "        side_num = random.randint(0,1)\n",
    "        second_color_side_up = second_card[side_num]\n",
    "        second_color_side_down = second_card[1-side_num]\n",
    "        \n",
    "        if second_color_side_up == 'W':\n",
    "            n_trials += 1\n",
    "            if first_color_side_down == 'B':\n",
    "                n_success += 1\n",
    "                \n",
    "n_success/n_trials"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2H1.** Suppose there are two species of panda bear. Both are equally common in the wild and live in the same places. They look exactly alike and eat the same food, and there is yet no genetic assay capable of telling them apart. They differ however in their family sizes. Species A gives birth to twins 10% of the time, otherwise birthing a single infant. Species B births twins 20% of the time, otherwise birthing singleton infants. Assume these numbers are known with certainty, from many years of field research.\n",
    "\n",
    "Now suppose you are managing a captive panda breeding program. You have a new female panda of unknown species, and she has just given birth to twins. What is the probability that her next birth will also be twins?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "If a panda's first birth is twins, the second birth is twins 16.66% of the time.\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd # I'm joking\n",
    "pandas = ('A', 'B')\n",
    "p_twins = {'A':.10, 'B':.20}\n",
    "n_twins = 0\n",
    "n_success = 0\n",
    "n_sims = 10**6\n",
    "\n",
    "while n_twins < n_sims:\n",
    "    panda = random.choice(pandas)\n",
    "    if random.random() <= p_twins[panda]:\n",
    "        n_twins += 1\n",
    "        if random.random() <= p_twins[panda]:\n",
    "            n_success += 1\n",
    "            \n",
    "percentage = round((n_success/n_twins)*100, 2)\n",
    "print(f'If a panda\\'s first birth is twins, the second birth is twins {percentage}% of the time.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2H2.** Recall all the facts from the problem above. Now compute the probability that the panda we have is from species A, assuming we have observed only the first birth and that it was twins."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.332929"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "panda_counts = {panda:0 for panda in pandas}\n",
    "n_twins = 0\n",
    "\n",
    "while n_twins < n_sims:\n",
    "    panda = random.choice(pandas)\n",
    "    if random.random() <= p_twins[panda]:\n",
    "        n_twins += 1\n",
    "        panda_counts[panda] += 1\n",
    "        \n",
    "panda_counts['A']/n_sims"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2H3.** Continuing on from the previous problem, suppose the same panda mother has a second birth and that it is not twins, but a singleton infant. Compute the posterior probability that this panda is species A."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2H4.** A common boast of Bayesian statisticians is that Bayesian inference makes it easy to use all of the data, even if the data are of different types. \n",
    "\n",
    "So Suppose now that a veterinarian comes along who has a new genetic test that she claims can identify the species of our mother panda. But the test, like all tests, is imperfect. This is the information you have about the test:\n",
    "\n",
    "* The probability it correctly identifies a species A panda is 0.8.\n",
    "* The probability it correctly identifies a species B panda is 0.65.\n",
    "\n",
    "The vet administers the test to your panda and tells you that the test is positive for species A. First ignore your previous information from the births and compute the posterior probability that your panda is species A. Then redo your calculation, now using the birth data as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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